Tilings of the Sphere with Right Triangles I: The Asymptotically Right Families

Robert J. MacG. Dawson, Blair Doyle

Abstract

Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper determines which right spherical triangles within certain families can tile the sphere.